Question

Wiseman Video plans to make four annual deposits of $2,250 each to a special building fund. The fund’s assets will be invested in mortgage instruments expected to pay interest at 12% on the fund’s balance. (FV of $1, PV of $1, FVA of $1, PVA of $1, FVAD of $1 and PVAD of $1) (Use appropriate factor(s) from the tables provided.) Determine how much will be accumulated in the fund on December 31, 2024, under each of the following situations.

The first $2,250 deposit is made on December 31, 2021, and interest is compounded annually.

The first $2,250 deposit is made on December 31, 2020, and interest is compounded annually.

The first $2,250 deposit is made on December 31, 2020, and interest is compounded quarterly.

The first $2,250 deposit is made on December 31, 2020, interest is compounded annually, and interest earned is withdrawn at the end of each year.

Answer 1

Solution 1:

Future value = $2,250 * Cumulative FV factor at 12% for 4 periods of ordinary annuity = $2,250 * 4.77933 = $10,753

Solution 2:

Future value = $2,250 * Cumulative FV factor at 12% for 4 periods of annuity due = $2,250 * 5.35285 = $12,044

Solution 3:

Quarterly interest rate = 12% / 4 =3%

Effective annual interest rate = 1 (1+0.03)^4 - 1 = 12.55%

Future value = $2,250 * Cumulative FV factor at 12.55% for 4 periods of annuity due = $2,250 * 5.42263 = $12,201

Solution 4:

If interest earned is withdrawn at the end of year then accumulated fund balance = $2,250 * 4 = $9,000